This paper describes the problem of lineal filtering of noisy data under a Maximum Likelihood objective. In this sense, the paper shows that a weighted square error cost function deals and it is necessary to weight the filtering error sequence by a factor that, basically, depends the probability density function of the error sequence and on its first derivate. As it is well known, this information used to be not available and other proposals must be made. For this purpose, going around this problem, the paper discusses the design of this weighting factor for including sorne kind of data-selection mechanism for the final filter weight-vector solution design. The underlying of the proposal is the development of a recursive algorithm in such a way that for any measure or observation, its associated